Final answer:
The correct distance for an 8-minute time difference between shear and compression waves is actually 1440 km. The provided options are incorrect as none match the calculation result obtained by solving the equations for the speeds of P-waves and S-waves and their respective arrival times.
Step-by-step explanation:
The question pertains to the time difference between shear (S-wave) and compression (P-wave) waves, which are seismic waves generated during an earthquake. The speed of P-waves is typically around 6 km/s, and S-waves travel at about 2 km/s. To find the distance at which there would be an 8-minute (or 480-second) difference in arrival time, we use the formula:
Distance = Speed × Time Difference
Since we have two waves traveling at different speeds, we'll set up two equations to represent each wave's travel:
D = 6 km/s × t for P-waves
D = 2 km/s × (t + 480) for S-waves
Given that the distances D from the epicenter to the point are the same for both waves, we can set the two equations equal to each other and solve for t:
6 km/s × t = 2 km/s × (t + 480)
2 km/s × t + 2 km/s × 480 = 6 km/s × t
960 km = 4 km/s × t
t = 240 seconds
Now, we substitute the value of t back into one of our original equations:
6 km/s × 240 s = 1440 km
So, the correct distance for an 8-minute time difference between the shear and compression waves is 1440 km. Therefore, none of the provided options A, B, C, or D are correct.